hi is there any1 who can show me how to do this q.
Q.Show that a relation R on a set X is transitive if and only if there are directed edges from x to y and from y to z in the digraph of R there is a directed edge from x to z? :confused: :confused: :confused: :eek:

Aug 17th 2006, 04:41 AM

ThePerfectHacker

Quote:

Originally Posted by dcapdogg

hi is there any1 who can show me how to do this q.
Q.Show that a relation R on a set X is transitive if and only if there are directed edges from x to y and from y to z in the digraph of R there is a directed edge from x to z? :confused: :confused: :confused: :eek:

You can speak of a graph,
G=(X,R) because R is a subset of a two-element power set of X. But since R is transitive on X implies that if (x,y) in R and (y,z) in R then (x,z) in R, same as being viewed as a digraph on X having this property.